Finding angles in Barycentric system

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How to find the angles of a triangle given the barycentric coordinates of its corners? Does it work if i take the first two components of every coordinate, and find the angles in the triangle (on the cartesian plane) determined by those coordinates?

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The barycentric coordinates of the corners of any triangle are always

$$[1:0:0] \qquad [0:1:0] \qquad [0:0:1]$$

So there is no angle information available. It tells you nothing about the shape of the triangle.